def endPointGradient(self, testGradient=False):
rg, N, T = self.getSimData()
interp_loc = self.xt[:,:,T-1].copy()
(interp_target, d_interp) = kernelMatrix_fort.applyk_and_diff( \
interp_loc, rg.nodes, self.dual_target,
self.khs, self.kho, self.rg.num_nodes)
diff = self.m[:,T-1] - interp_target
dx = numpy.zeros((rg.num_nodes, 3))
dm = 2*diff*self.J[:,T-1]
for k in range(3):
dx[:,k] = 2.*diff*self.J[:,T-1] \
*(-1)*d_interp[:,k]
dJ = diff * diff
dx *= self.g_eps * rg.element_volumes[0]
dm *= self.g_eps * rg.element_volumes[0]
dJ *= self.g_eps * rg.element_volumes[0]
# test the endpoint gradient
if testGradient:
objOld = self.objectiveFun()
eps = 1e-8
x = self.xt[:,:,T-1]
m = self.m[:,T-1]
J = self.J[:,T-1]
xr = numpy.random.randn(x.shape[0], x.shape[1])
mr = numpy.random.randn(m.shape[0])
jr = numpy.random.randn(J.shape[0])
x1 = self.xt[:,:,T-1] + eps * xr
m1 = self.m[:,T-1] + eps * mr
J1 = self.J[:,T-1] + eps * jr
interp_target = kernelMatrix_fort.applyk(x1, rg.nodes, self.dual_target, self.khs, self.kho, self.rg.num_nodes)
diff = m1 - interp_target.real
sqrtJ = numpy.sqrt(J1)
objFun = numpy.dot(diff*sqrtJ, sqrtJ*diff) * self.g_eps * \
rg.element_volumes[0]
ip = numpy.multiply(dx, xr).sum(axis=1).sum() \
+ numpy.dot(dm, mr) \
+ numpy.dot(dJ, jr)
logging.info("Endpoint gradient test: %f, %f" % \
((objFun - objOld)/eps, ip))
if (self.verbose_file_output):
rg.create_vtk_sg()
rg.add_vtk_point_data(diff.real, "diff")
rg.add_vtk_point_data(d_interp.real, "d_interp")
rg.add_vtk_point_data(self.J[:,T-1], "J")
rg.add_vtk_point_data(dJ, "dJ")
rg.add_vtk_point_data(self.target, "target")
rg.add_vtk_point_data(interp_target, "interp_target")
rg.add_vtk_point_data(dm.real, "dm")
rg.add_vtk_point_data(self.m[:,T-1], "m")
rg.add_vtk_point_data(dx.real, "dx")
rg.vtk_write(0, "grad_test", output_dir=self.output_dir)
return [dx, dm, dJ]
def __init__(self, output_dir, config_name, letter_match=None):
self.num_points = None
self.domain_max = None
self.dx = None
self.verbose_file_output = False
self.output_dir = output_dir
self.spline_interp = False
# used only for letter examples
self.letter_match = letter_match
smoothImageConfig.configure(self, config_name)
self.rg = regularGrid.RegularGrid(self.dim, self.num_points, \
self.domain_max, self.dx, "meta")
self.times = numpy.linspace(self.time_min, self.time_max, \
self.num_times)
self.dt = (self.time_max - self.time_min) / (self.num_times - 1)
self.optimize_iteration = 0
self.g_eps = 1.
logging.info("sigma: %f" % self.sigma)
logging.info("sfactor: %f" % self.sfactor)
logging.info("num_points: %s" % str(self.rg.num_points))
logging.info("domain_max: %s" % str(self.rg.domain_max))
logging.info("dx: %s" % str(self.rg.dx))
logging.info("dt: %f" % self.dt)
rg = self.rg
self.x0 = self.rg.nodes.copy()
self.xt = numpy.zeros((rg.num_nodes, 3, self.num_times))
self.v = numpy.zeros((rg.num_nodes, 3, self.num_times))
self.m = numpy.zeros((rg.num_nodes, self.num_times))
self.z = numpy.zeros((rg.num_nodes, 3, self.num_times))
self.J = numpy.ones((rg.num_nodes, self.num_times))
self.id_x = self.rg.nodes[:,0].copy()
self.id_y = self.rg.nodes[:,1].copy()
self.m = numpy.zeros((rg.num_nodes, self.num_times))
self.alpha = numpy.zeros(rg.num_nodes)
self.alpha_state = numpy.zeros_like(self.alpha)
rg.create_vtk_sg()
rg.add_vtk_point_data(self.template_in, "template_in")
rg.add_vtk_point_data(self.target_in, "target_in")
rg.vtk_write(0, "images", output_dir=self.output_dir)
if self.spline_interp:
si = SplineInterp(rg, self.KH, self.template_in)
self.dual_template = si.minimize()
si = SplineInterp(rg, self.KH, self.target_in)
self.dual_target = si.minimize()
else:
self.dual_template = self.template_in.copy()
self.dual_target = self.target_in.copy()
(templ, dtempl) = kernelMatrix_fort.applyk_and_diff( \
rg.nodes, rg.nodes, self.dual_template,
self.khs, self.kho, self.rg.num_nodes)
self.target = kernelMatrix_fort.applyk( \
rg.nodes, rg.nodes, self.dual_target,
self.khs, self.kho, self.rg.num_nodes)
self.template = templ
self.D_template = dtempl
if True:
temp = numpy.zeros(rg.num_nodes)
temp[50] = 1.
kvt = kernelMatrix_fort.applyk( \
rg.nodes, rg.nodes, temp,
self.kvs, self.kvo, self.rg.num_nodes)
kht = kernelMatrix_fort.applyk( \
rg.nodes, rg.nodes, temp,
self.khs, self.kho, self.rg.num_nodes)
rg.create_vtk_sg()
rg.add_vtk_point_data(self.template, "template")
rg.add_vtk_point_data(self.D_template, "D_template")
rg.add_vtk_point_data(self.target, "target")
rg.add_vtk_point_data(kvt, "kvt")
rg.add_vtk_point_data(kht, "kht")
rg.vtk_write(0, "initial_data", output_dir=self.output_dir)
tmpMax = numpy.max(numpy.abs(self.template))
tarMax = numpy.max(numpy.abs(self.target))
self.template /= tmpMax
self.dual_template /= tmpMax
self.target /= tarMax
self.dual_target /= tarMax
def __init__(self, output_dir, config_name, letter_match=None):
self.num_points = None
self.domain_max = None
self.dx = None
self.verbose_file_output = False
self.output_dir = output_dir
self.spline_interp = False
self.noJ = True
self.unconstrained = False
# used only for letter examples
self.letter_match = letter_match
smoothImageConfig.configure(self, config_name)
self.rg = regularGrid.RegularGrid(self.dim, self.num_points, \
self.domain_max, self.dx, "meta")
self.times = numpy.linspace(self.time_min, self.time_max, \
self.num_times)
self.dt = (self.time_max - self.time_min) / (self.num_times - 1)
self.optimize_iteration = 0
self.g_eps = 1.
self.khSmooth =0.2*numpy.asarray(self.rg.dx).max() # self.khs/2
logging.info("sigma: %f" % self.sigma)
logging.info("sfactor: %f" % self.sfactor)
logging.info("num_points: %s" % str(self.rg.num_points))
logging.info("domain_max: %s" % str(self.rg.domain_max))
logging.info("dx: %s" % str(self.rg.dx))
logging.info("dt: %f" % self.dt)
logging.info('khSmooth: %f'% self.khSmooth)
rg = self.rg
self.x0 = self.rg.nodes.copy()
self.xt = numpy.zeros((rg.num_nodes, 3, self.num_times))
self.v = numpy.zeros((rg.num_nodes, 3, self.num_times))
self.m = numpy.zeros((rg.num_nodes, self.num_times))
self.z = numpy.zeros((rg.num_nodes, 3, self.num_times))
self.id_x = self.rg.nodes[:,0].copy()
self.id_y = self.rg.nodes[:,1].copy()
self.m = numpy.zeros((rg.num_nodes, self.num_times))
self.alpha = numpy.zeros(rg.num_nodes)
self.alpha_state = numpy.zeros_like(self.alpha)
if self.unconstrained:
self.noJ = True
self.z0 = numpy.zeros((rg.num_nodes, 3))
self.z0weight = 100*numpy.ones((rg.num_nodes,1))
self.z0_state = numpy.zeros((rg.num_nodes, 3))
if not self.noJ:
self.J = numpy.ones((rg.num_nodes, self.num_times))
rg.create_vtk_sg()
rg.add_vtk_point_data(self.template_in, "template_in")
rg.add_vtk_point_data(self.target_in, "target_in")
rg.vtk_write(0, "images", output_dir=self.output_dir)
if self.spline_interp:
trg = kernelMatrix_fort.applyk( \
rg.nodes, rg.nodes, self.target_in,
self.khs/4, self.kho, self.rg.num_nodes)
tpl = kernelMatrix_fort.applyk( \
rg.nodes, rg.nodes, self.template_in,
self.khs/4, self.kho, self.rg.num_nodes)
self.khSmooth = self.khs
logging.info('RKHS Projection Template')
si = SplineInterp(rg, self.khs, self.kho, tpl,True)
self.dual_template = si.minimize()
logging.info('RKHS Projection Target')
si = SplineInterp(rg, self.khs, self.kho, trg)
self.dual_target = si.minimize()
else:
self.dual_template = self.template_in.copy()
self.dual_target = self.target_in.copy()
(templ, dtempl) = kernelMatrix_fort.applyk_and_diff( \
rg.nodes, rg.nodes, self.dual_template,
self.khSmooth, self.kho, self.rg.num_nodes)
self.target = kernelMatrix_fort.applyk( \
rg.nodes, rg.nodes, self.dual_target,
self.khSmooth, self.kho, self.rg.num_nodes)
self.template = templ
self.D_template = dtempl
if True:
temp = numpy.zeros(rg.num_nodes)
temp[rg.num_nodes/2 + rg.num_points[1]/2] = 1.
kvt = kernelMatrix_fort.applyk( \
rg.nodes, rg.nodes, temp,
self.kvs, self.kvo, self.rg.num_nodes)
kht = kernelMatrix_fort.applyk( \
rg.nodes, rg.nodes, temp,
self.khs, self.kho, self.rg.num_nodes)
rg.create_vtk_sg()
rg.add_vtk_point_data(self.template, "template")
rg.add_vtk_point_data(self.D_template, "D_template")
rg.add_vtk_point_data(self.target, "target")
rg.add_vtk_point_data(kvt, "kvt")
rg.add_vtk_point_data(kht, "kht")
rg.vtk_write(0, "initial_data", output_dir=self.output_dir)
tmpMax = numpy.max(numpy.abs(self.template))
tarMax = numpy.max(numpy.abs(self.target))
self.D_template /= tmpMax
self.template /= tmpMax
self.dual_template /= tmpMax
self.target /= tarMax
self.dual_target /= tarMax
self.z0weight[:] = numpy.sqrt(1e-6 + (self.D_template**2).sum(axis=1)[..., numpy.newaxis])